Question: What is the amplitude of $g(x)=8\cos\left(5\pi x+\dfrac{3\pi}{2}\right)-9$ ?
Solution: Amplitude in sinusoids of the form $f(x)=a\cos(bx+c)+d$ The amplitude of a sinusoid of the form $f(x)={a}\cos(bx + c) + d$ is equal to $|{a}|$. [How can we justify this given our graphical understanding of amplitude?] Finding the amplitude The amplitude of $g(x) = {8}\cos\left(5\pi x+\dfrac{3\pi}{2}\right)-9$ is $|{8}|=8$.